Question

In the following question, a is a real number. Question: what choice of a would yield a system of linear equations with NO solutions?

9x-14y=-3

2x-ay=-6

Answer 1

Answer: The value of a should be 3.11.

Explanation:

Since we have given that

`9x-14y=-3\\\\2x-ay=-6`

We need to find the value of a so that it would yield a system of linear equations with NO solutions.

As we know the condition of no solutions, it means the lines should be parallel.

i.e.

`(a_1)/(a_2)=(b_1)/(b_2)\\eq (c_1)/(c_2)`

Consider the first two terms:

`(9)/(2)=(-14)/(-a)\\\\a=(2* 14)/(9)\\\\a=3.11`

So, the value of a should be 3.11.